A great deal of research has been performed on a so-called "generalized partial response signaling (GPRS)" technique. This technique is used in a communications system to prevent a transmitted signal from being adversely affected by intersymbol interference incurred in a communications channel. As is well known, the intersymbol interference results from the fact that a typical communications channel inherently has memory such that the signals previously transmitted through the channel interfere with the current, transmitted signal. In accordance with the GPRS technique, a nonlinear filtering device is employed in the transmitter to precode the signal to be transmitted, and this precoding process effects a compensation for the ensuing intersymbol interference affecting such signal. Details on the GPRS technique can be found in: M. Tomlinson, "New Automatic equalizer employing modulo arithmetic," Electron. Lett., Vol. 7, nos. 5/6, March 1971, pages 138-139; H. Harashima and H. Miyakawa, "Matched-transmission technique for channels with intersymbol interference," IEEE Trans. Commun., Vol. COM-20, August 1972, pages 774-780 and J. Mazo and J. Salz, "On the Transmitted Power in Generalized Partial Response," IEEE Trans. Commun., Vol. Com-24, March 1976, pages 348-352, all of which are hereby incorporated by reference.
There are arrangements in the prior art which involve the use of the GPRS technique, coupled with transmission of signal points selected from a multidimensional signal constellation wherein the signal points are regularly spaced. An example of such arrangements is disclosed in a copending U.S. patent application Ser. No. 439,134, entitled "Technique for Achieving the Full Coding Gain of Encoded Digital Signals" and filed on Nov. 20, 1989, which is hereby incorporated by reference. Invariably, after these prior-art arrangements process the selected signal points using the above-mentioned precoding process, the resulting signal points to be transmitted spatially occupy a square region. As a consequence, the average transmission power required to transmit these resulting signal points are oftentimes undesirably higher than the average signal power required by the signal constellation used. Although this increase in the average power can be avoided by using signal constellations having a square shape, the sizes of the square constellations are, however, limited to N.sup.2 and 2N.sup.2 signal points, where N is an even integer. As a result, the square constellations, because of their particular sizes, do not always allow the full utilization of a given channel capacity.
Accordingly, it is desirable to have other signal constellations which, like the square constellations, each call for an average transmission power no more than the average signal power required by the signal constellation when used with the GPRS technique.